Actually a 1d point is entirely logical in the dichotomy of "being" and "nonbeing", which is a foundation in mathematics.

Yes, but mathematics is just a conceptual/theoretical man-made tool. To allow yourself to forget that the laws of physics don't apply to imagination is to allow yourself to remain strictly in the theoretical realm. It's a closed system without a feedback loop from external reality.

There are no such things as "error in imagination" so anything goes. Ramanujan proved that 1+2+3+4+... = -1/12

But in the physical realm you have to worry about negative consequences as there are such things as errors and limits as to what is possible.

Eodnhoj wrote:
All numbers exist as points in space . All points are the same

If I take I point and halve it I get 2 of the same points

If I take these 2 points which exist as I point and halve it I get 8 points

The number line does not exist in space because it is entirely abstract so therefore requires no space at all
And because it is abstract it does not require points either even if you define a point as having zero volume
Even though both the number lines [ standard / complex ] extend to infinity and there are multiple infinites

Every number on the number line occupies a unique fixed place so in that respect it cannot be altered in any way
A number can therefore only be halved for example when it exists as a separate entity not part of the number line

So you can say halve 6 to get 3 when 6 exists by itself in total isolation but when it is on the number line it cannot be altered in any way
And even though 2 X 3 = 6 there is also only one 3 on the number line not two because there is only one space for each individual number

Actually a 1d point is entirely logical in the dichotomy of "being" and "nonbeing", which is a foundation in mathematics.

Yes, but mathematics is just a conceptual/theoretical man-made tool. To allow yourself to forget that the laws of physics don't apply to imagination is to allow yourself to remain strictly in the theoretical realm. It's a closed system without a feedback loop from external reality.

There are no such things as "error in imagination" so anything goes. Ramanujan proved that 1+2+3+4+... = -1/12

But in the physical realm you have to worry about negative consequences as there are such things as errors and limits as to what is possible.

It may be a man made tool, but men use tools to form them and effectively it acts as a form of adaptation.

The laws of physics are obscure...just like math for that matter. Math forms the frameworks of physics, physics forms the framework of math. Failed theory is merely an abstract framework not aligning with an empirical one.

There is no such thing as an error in "physics" either considering physics is strictly a localization of empirical movements...nothing more. The "laws as localizations" thread in the "metaphysics?" section covers this.

Negative consequences are entirely theoretical if the physical universe realigns to any potential warp in it.

Link for ramanujan's proof?

I have argued all progressive whole number lines are simultaneously directed to point 0. It is logically possible for what he argues.

Eodnhoj wrote:
All numbers exist as points in space . All points are the same

If I take I point and halve it I get 2 of the same points

If I take these 2 points which exist as I point and halve it I get 8 points

The number line does not exist in space because it is entirely abstract so therefore requires no space at all
And because it is abstract it does not require points either even if you define a point as having zero volume
Even though both the number lines [ standard / complex ] extend to infinity and there are multiple infinites

Every number on the number line occupies a unique fixed place so in that respect it cannot be altered in any way
A number can therefore only be halved for example when it exists as a separate entity not part of the number line

So you can say halve 6 to get 3 when 6 exists by itself in total isolation but when it is on the number line it cannot be altered in any way
And even though 2 X 3 = 6 there is also only one 3 on the number line not two because there is only one space for each individual number

Abstraction is the closest thing to "empty space" we understand...or rather "space" but "empty" can be applied for some as well.

The progressive nature of numbers, as having a linear nature of the actual number line and the "form/function" of logic which produces them, is inseparable from a spatial entity.

The number line is composed of halving, it's inherent nature is contradiction by dualistic opposition:

1 → 2 = 1 → 1/2

a. Where each 1/2 of a point is equivalent to a doubling of the point

1 → 3 = 1 → 1/3

a. because 1 progressing to 1/2 and 2 observes 1 directed to this very same 1/2 and 2 as 1/3 and 3.
b. Because 1 always splits between 1 and Many, it is founded upon a contradictory "halving".

1. All numbers exist as points in space. All points are the same; hence all points exist as one point.

Sorry, but no. Logically, you cannot claim much more than:

All numbers exist as points at various coordinates in space. All points are identical; therefore, all numbers exist as identical points at various coordinates in space.

Therefore the remainder of your post is unfounded.

Actually if all points are effectively the same point, approximated through many points, then by default I can claim more than that.

The corridinate is merely a position of one point relative to another, however those positions are effectively 1 point observed approximately through many. The "field" which gives an apparent seperation of these "1" points effectively is void.

Now this breaks down to a basic yin/yang type dualism. If the coordinates are 0d points then we are left with a 1d point field. The same occurs if the coordinates are a 1d point, we are left with a 0d point field.
****See "do points act as fields" thread in the...I think it is metaphysics section.

Without these foundations you posts are illogical as we are left with corridinates, as 0d points, and the surrounding as non-zero points equivalent to a 1 dimensionality.

The number line alone necessitates the prime foundation of number as point space, both rationally and intuitively.

I would argue that the coordinate defines the point. No coordinates - no point.

Definition gives birth.

Circularity: corridinates are also defined by the point.

In a seperate respect a standard definition of the point, as 0d, negates definition.

It can appeal to the law of identity, however the law of identity has issues as well, I address that elsewhere (epistemology, if memory serves, "new laws of identity"/"contradiction in laws of identity")

A point is a point is a point, under standard defintion it is always 0d. Even under a theoretical 1d nature it is still the same.

So if it is a matter of choice the axioms can be chosen, allowing further axioms. In a separate respect the axioms are subject to bandwagon fallacy.

Yes. Axiomatic reasoning is an elaborate exercise in combinatorics. You tweak the axioms and see what patterns emerge. Some of those patterns are practically useful in the real world.

The first "axiom" (pre-supposition) on which logic is based is that the world has structure and is governed by rules. The fact that we are observing structure/rules could be entirely coincidental. A temporary statistical anomaly.

Actually all lines are both composed of and composing further lines/points by definition. Each line is a quantification of infinite lines. Each point is a quantification of infinite points.

Conceptually - yes.

In line with counter-factual reasoning you ought to assume that there is non-zero chance the first pre-supposition of logic is wrong. e.g that the universe has no structure whatsoever. In which case logic is entirely metaphysical. And predictive models work entirely by accident.

Either way - infinities. Those are abstract. Or rather - even if infinities exist, our representation of infinities is abstract/finite.

So if it is a matter of choice the axioms can be chosen, allowing further axioms. In a separate respect the axioms are subject to bandwagon fallacy.

Yes. Axiomatic reasoning is an elaborate exercise in combinatorics. You tweak the axioms and see what patterns emerge. Some of those patterns are practically useful in the real world.

The first "axiom" (pre-supposition) on which logic is based is that the world has structure and is governed by rules. The fact that we are observing structure/rules could be entirely coincidental. A temporary statistical anomaly.

Actually all lines are both composed of and composing further lines/points by definition. Each line is a quantification of infinite lines. Each point is a quantification of infinite points.

Conceptually - yes.

In line with counter-factual reasoning you ought to assume that there is non-zero chance the first pre-supposition of logic is wrong. e.g that the universe has no structure whatsoever. In which case logic is entirely metaphysical. And predictive models work entirely by accident.

Either way - infinities. Those are abstract. Or rather - even if infinities exist, our representation of infinities is abstract/finite.

A temporary statistical anomaly still necessitates statistics, through fractions fundamentally as all statistics are fractions, as a constant.

Infinities are unprovable, except through pure geometric axioms, but act as the foundation of proof.